Question

show that sin^-1(2x✓1-x^2)

Answer 1

Letx=sin a, So, (a=sin^-1x) -(1)
=LHS
=sin^-1(2sin a√1-sin^2 a)
=sin^-1(2sin a√cos^2 a)
=sin^-1(2sin a cos a)
=sin^-1(sin2a)
[Comparing 'sin^-1' with 'sin']
We get,
=2a
From (1),
=2sin^-1x
RHS proved.